An immigration reform bill in the Senate scored the support of several Republicans after the sponsors of the legislation agreed on Thursday to add a "surge" of border enforcement to their plan.

But after making the deal, Democrats stressed one key point: while the agreement will call for more border enforcement, it won't block the path to citizenship for the country's 11 million undocumented immigrants.

Sen. Charles Schumer (D-N.Y.), one of the architects of the bill, spoke to Univision News anchor Jorge Ramos in an interview set to air in full on the political show "Al Punto" this Sunday.

"We all want border security, but we didn't want border security [to] be used as a pretext to block the path to citizenship, and that was what the fight was," Schumer said. "We overcame that a couple of days ago where we said we were not having any of these 'triggers' that are not attainable on border security, which would prevent the earned path to citizenship."

The deal is designed to appeal to Republican senators who think the legislation doesn't go far enough on immigration enforcement.

The new border security provision, drafted by Sens. John Hoeven (R-N.D.) and Bob Corker (R-Tenn.), would double the number of Border Patrol agents, implement an entry/exit visa tracking system and employer verification program, and call for the completion of 700 miles of border fence.

The language would add to an existing border security plan in the Senate bill that must be put into place before most undocumented immigrants can get permanent legal status. The additional border agents would tack $30 billion more onto the cost of the bill, The Washington Post reported.

The Senate defeated another proposal from Sen. John Cornyn (R-Texas) earlier on Thursday that would have also imposed stricter border security measures.

The Cornyn amendment would have required the Southern border to be under "operational control" before undocumented immigrants could become legal permanent residents. Democrats called it a "poison pill," saying it would block the path to citizenship.

Democrats on the bipartisan "Gang of Eight" that drafted the legislation made it clear they were not in love with the newer language, but said they were willing to accept it in the interest of building more support for the legislation.

That's because they want a strong show of support for the plan as it leaves the Senate. The idea is that a good showing in the Senate will give the bill legs when it arrives in the Republican-controlled House of Representatives.

One of the Republican "gang" members, Sen. Jeff Flake (Arizona), spoke about that with Univision News' Jorge Ramos.

"We've had enough Republicans to pass the bill, but we want it to be overwhelming," Flake said. "In order to do that, you have to have a bill that's strong on some of the elements that Republicans find important, particularly border security."